Landau Constant
N.B. A detailed on-line essay by S. Finchwas the starting point for this entry.
Let 
be the set of Complex analytic functions 
defined on an open region containing theclosure of the unit disk 
satisfying 
and 
. For each in , let 
be theSupremum of all numbers 
such that 
contains a disk of radius . Then
This constant is called the Landau constant, or the Bloch-Landau Constant. Robinson (1938, unpublished) andRademacher (1943) derived the bounds
where
is the Gamma Function, and conjectured that the second inequality is actually an equality,
See also Bloch Constant
References
Finch, S. ``Favorite Mathematical Constants.'' http://www.mathsoft.com/asolve/constant/bloch/bloch.html Rademacher, H. ``On the Bloch-Landau Constant.'' Amer. J. Math. 65, 387-390, 1943.
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